The Stone Skeleton: A Reappraisal

Round 1

Reviewer 1 Report

It would be nice to explain how the hinges develop in the arches, given the assumption at paragraph 5, 1) Masonry has no tensile capacity.

In the figures such as Milan Cathedral, a plan view and section views of the building could be useful to understand the reasons of the several cracks mentioned. In Fig. 2, 3 instead of calling "compression failure" maybe it is better to call them a "tension or shear failure" because the small strength of the masonry; and a compression failure is evidenced by crushing of the cross section, which is not visible.

Before Fig. 8 there is a paragraph beginning with Table 8. from Amodio, ..... This is a mistake in the writing of the Commentary, perhaps should be deleted.

Author Response

First comment: We have included a brief explanation.  

We have added a figure as a key plan for Figure 2 and 3 

Comment on Figure 2 and 3 

Figure 2: while the cracks result from internal tension, there is no transverse traction, and they are clearly splitting tension resulting from excessive compression.  Since the cracks are vertical, there is no evidence of any shear involvement.

Figure 3: the cracks are based on material failure, which contradicts Heyman's assumption.  Although the cracking mode is complicated, we concur with the reviewer that they can be identified as some combination of compression and shear.  The text has been modified.    

'Table 8' corrected to Figure 8.

Reviewer 2 Report

The paper is an interesting reappraisal of Heyman's fundamental 1966 article.

It focuses mainly on the consequences of the non-critical application of limit analysis to masonry arches, without verifying that the starting assumptions are still valid.

Numerous examples of the loss of validity of the Heyman's assumptions, namely unlimited compressive and shear strength, are presented, as well as an extensive bibliography on the subject. 

However, the authors do not arrive at an alternative formulation of an analysis method, nor do they provide a quantitative demonstration of the error that can occur in calculating the ultimate load in these cases: maybe some numerical examples in support of their theses would be helpful.

Some minor remarks, please correct:

page 8, table 8 is missing

page 11, references: 
Cardani and Bassetti is badly written, also missing conference name;
Heyman 1993 is badly formatted?

page 12:
must be Riveiro, B. (not B. Riveiro); Rios ... must be before Riveiro.
Zampiero, Amoroso and Pellegrino 2019 is repeated after two lines with the doi added.

Author Response

request for numerical examples:

Some comparison of effects is already available in the references or in the commentary.  The effect of including a small allowable tensile stress is described numerically in Boothby and Fanning (2004) and Fanning and Boothby (2011) and Ng, Fairfield, and Sibbald (1999).  The results of the latter are summarized in the article.  The strengthening effect of a spandrel wall is discussed in Amodio, Gilbert, and Smith (2019), whose results are already included in the manuscript.  The incorporation of masonry sliding or creep into a comprehensive model and the development of numerical results would be an entire, separate study beyond the scope of this brief commentary:.

'Table 8' has been fixed 

Cardani and Massetti reference corrected. 

Reveiro reference corrected

Zampieri.... reference corrected